常曲率空间中子流形的无穷小Ⅱ—等距理论

THE THEORY OF INFINITESIMAL I —ISOMETRYON THE SUBMANIFOLDS OF A SRACEWITH CONSTANT CURVATURE

在本文中,我们着重研究了常曲率空间中子流形的无穷小Ⅱ—等距问题。所得到定理都是新的,而且把E^3中的某些经典结果推广到了常曲率空间中具有高余维数的子流形上。

Inthis paper , we consider the infinitesimal I -iso-metry def6rmations of submanifolds immersed in a space form N of constant curvature. We obtain some reswlts which are new even in the case of N being the Euc -lidean space. At the same time,we generalize some classical results in E3 to higher codimension sub -manifolds immersed in a space form of constant cur -vature.